+0  
 
0
60
1
avatar

A whispering chamber is an elliptically arched chamber. A unique feature of a whispering chamber is that when a person standing at one focus of the ellipse whispers, he can be heard by a person standing at the other focus, regardless of the dimensions of the ellipse from which the dome is built.

Suppose that the dimensions of the ellipse used to create a whispering dome is 200 feet by 380 feet. Walter stands at one focus, and Barbara stands at the other focus.

How far apart are Walter and Barbara?

Enter your answer, rounded to the nearest tenth of a foot.

 Jan 15, 2021
 #1
avatar+116126 
+1

Assuming that  the  wider part of the ellipse is horizontal  and the center is (0,0)

 

a = 380/2 =   190

b =  200/2  = 100

 

So  we  have this form

 

x^2/ 190^2   + y^2/100^2 =   1

 

The focal distance  from the center  is given  by

 

sqrt  [ a^2 - b^2 ]  =  sqrt  [ 190^2 - 100^2  ]  =  sqrt [26100]   = 30sqrt (29)

 

So....Walter and Barbara  are standing    2 * 30sqrt (29)  =  60sqrt (29) ≈   323.1  ft  apart

 

See the graph here : https://www.desmos.com/calculator/62jlku7yf3

 

 

cool cool cool

 Jan 15, 2021

83 Online Users

avatar
avatar
avatar